Chapter 8.1, Problem 47E

To determine

To Find: The reason for why the four legged chair may rock from side to side even if the floor is level and determine, would a three legged chair on the same level floor rock from side to side why or why not.

Answer to Problem 47E

The required table is shown in Table 2 number of no three planes define the point such that the leg of the three legged chair is always met in the final plane of the floor.

Explanation of Solution

For the plane that are not on the same line there is only one plane and one can use the three points that are not on the same line to name a plane.

Since, the three legs of the chair will be on the floor to define the plane but the point at the bottom of the fourth leg may not be in the same plane.

The case when the chair tips in a way that the leg is on the floor then the plane that is defined by this leg and the other two legs closest to it now lies in the plane of the floor.

Thus, the number of no three planes define the point such that the leg of the three legged chair is always met in the final plane of the floor.